Question

Simplify this problem for me

Answer 1

`\displaystyle E=e^(5x)`

Explanation:

Exponentials

Properties of exponentials:

`x^ax^b=x^(a+b)`

`(x^a)/(x^b)=x^(a-b)`

Simplify:

`\displaystyle E=(e^(-2)\cdot e^(2x+3))/(e^(1-3x))`

Multiplying in the numerator:

`\displaystyle E=(e^(-2+2x+3))/(e^(1-3x))=(e^(+2x+1))/(e^(1-3x))`

Applying the quotient:

`\displaystyle E=e^(2x+1-(1-3x))`

Operating:

`\displaystyle E=e^(2x+1-1+3x)`

Simplifying:

`\boxed{\displaystyle E=e^(5x)}`